Equilibrium constant from spectroscopic data

Van der Waals complexes can be observed spectroscopically by a variety of different teclmiques, including microwave, infrared and ultraviolet/visible spectroscopy. Their existence is perhaps the simplest and most direct demonstration that there are attractive forces between stable molecules. Indeed the spectroscopic properties of Van der Waals complexes provide one of the most detailed sources of infonnation available on intennolecular forces, especially in the region around the potential minimum. The measured rotational constants of Van der Waals complexes provide infonnation on intennolecular distances and orientations, and the frequencies of bending and stretching vibrations provide infonnation on how easily the complex can be distorted from its equilibrium confonnation. In favourable cases, the whole of the potential well can be mapped out from spectroscopic data. 

Gampp, H., Maeder, M., Meyer, C. J., Zuberbtihler, A. D. Calculation of equilibrium constants from multiwavelength spectroscopic data. 1. Mathematical considerations. Talanta 1985, 32, 95-101. 

H. Gampp, M. Maeder, C.J. Meyer and A.D. Zuberbuhler, Calculation of equilibrium constants from multiwavelength spectroscopic data. Ill Model-free analysis of spectrophotometric and ESR titrations. Talanta, 32 (1985) 1133-1139. 

BrCl (g). From spectroscopic data, Jost3 deduced values of the equilibrium constant at various temperatures, and computed for % Br2 (g) +iCl2(g)=BrCl(g), Q = 0.75. 

TRES appears to be a sensitive tool to follow lanthanide and actinide complexation in solution, because most of the spectroscopic parameters are influenced by complexation. It has been shown that caution should be paid to the type of photochemical processes occurring in solution in order to correctly analyse the data. Taking account this important point, TRES is an interesting technique for the determination of equilibrium constants. From a more fundamental viewpoint, one may wonder why inorganic ligands lead to regime A with U(VI) and to regime C with Cm(III). 

Two of its three adjustable parameters, De and re correspond to directly measurable molecular properties of bond dissociation energy and equilibrium interatomic distance respectively. The third parameter, a, is related to the force constants commonly used in spectroscopic analyses. A standard procedure [147] to obtain experimental potential energy curves is to calculate from spectroscopic data the constants ke, g, and j that appear in the expression... 

Since A1.2, the equilibrium constant for the dissociation of Br atoms, is known both experimentally and from spectroscopic data," it is possible... 

On the other hand, the Raman spectroscopic work suggests that such reactions are present. Evidently further work is needed to settle this issue. The review will use, without corrections, the equilibrium constant from the hydrobromic acid medium, in which the corrections for side-reactions would be fairly small. It should also be noted that the data from the hydrochloric acid medium have been subjected to an activity correction varying between 8.9 x 10 to 1.1 x 10. The review thus selects ... 

From the temperature variation of the equilibrium constant, thermodynamic parameters for the reaction were also obtained. The extent of formation of [Mo(CO)5l]" was found to be cation-dependent, and while equilibrium constants of 39 and 21 atm L moF were obtained for Bu4P and pyH+, none of the anionic iodide complex was observed for Na. Despite this variation, there seemed to be no correlation between the concentration of [Mo(CO)5l]" and the rate of the catalytic carbonylation reaction. It was proposed that [Mo(CO)5] and [Mo(CO)5l] are spectator species, with the catalysis being initiated by [Mo(CO)5]. Based on the in situ spectroscopic results and kinetic data, a catalytic mechanism was suggested, involving radicals formed by inner sphere electron transfer between EtI and [Mo(CO)5]. 

Based upon experimentally observed spectroscopic data, statistical thermodynamic calculations provide thermodynamic data which would not be obtained readily from direct experimental measurements for the species and temperature of interest to rocket propulsion. If the results of the calculations are summarized in terms of specific heat as a function of temperature, the other required properties for a particular specie, for example, enthalpy, entropy, the Gibb s function, and equilibrium constant may be obtained in relation to an arbitrary reference state, usually a pressure of one atmosphere and a temperature of 298.15°K. Or alternately these quantities may be calculated directly. Significant inaccuracies in the thermochemical data are not associated generaUy with the results of such calculations for a particular species, but arise in establishing a valid basis for comparison of different species. 

As 1 is a nonpolar symmetric top with symmetry, it should have no pure rotational spectrum, but it acquires a small dipole moment by partial isotopic substitution or through centrifugal distortion. In recent analyses of gas-phase data, rotational constants from earlier IR and Raman spectroscopic studies, and those for cyclopropane-1,1- /2 and for an excited state of the v, C—C stretching vibration were utilized Anharmonicity constants for the C—C and C—H bonds were determined in both works. It is the parameters, then from the equilibrium structure, that can be derived and compared from both the ED and the MW data by appropriate vibrational corrections. Variations due to different representations of molecular geometry are of the same magnitude as stated uncertainties. The parameters from experiment agree satisfactorily with the results of high-level theoretical calculations (Table 1). 

It is possible to distinguish between free ions from associated and covalently bonded species by conductivity measurements, because only free ions are responsible for electrical conductivity in solution [136, 399], Spectrophotometric measurements distinguish between free ions and ion pairs on the one hand, and covalent molecules on the other, because in a first approximation the spectroscopic properties of ions are independent of the degree of association with the counterion [141], The experimental equilibrium constant. Kexp, obtained from conductance data, may then be related to the ionization and dissociation constants by Eq. (2-16). 

Note that the equilibrium constant for reactions 3 and 4, namely Ks 4, may be calculable from spectroscopic and thermal data, so that hi = kz/Ks 4 may be calculated. This permits us to calculate kb = kA/kt and also the rate constant for reaction 6 (the reverse of h) from kb == kb/Kb e, where 7v is the cahiulable equilibrium constant. All of these data are given in Table XII.5. 

Although the data yield only the value of h and the ratio kikz/k2 [Eq. (XIII.18.2a)], the equilibrium constant X1.2 for reactions 1 and 2 can be calculated from thermodynamic and spectroscopic data, which then permits the rate constants k2 and h to be evaluated. In Arrhenius form, these are... 

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